Problem: Michael is 2 times as old as Stephanie. Fifteen years ago, Michael was 7 times as old as Stephanie. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Stephanie. Let Michael's current age be $m$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $m = 2s$ Fifteen years ago, Michael was $m - 15$ years old, and Stephanie was $s - 15$ years old. The information in the second sentence can be expressed in the following equation: $m - 15 = 7(s - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = 2s$ . Substituting this into our second equation, we get: $2s$ $-$ $15 = 7(s - 15)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $2 s - 15 = 7 s - 105$ Solving for $s$ , we get: $5 s = 90.$ $s = 18$.